Group GAP4(128,223)
Name: (Q8 : C8) : C2
Maximal quotients:GAP4(64,88) GAP4(64,100) GAP4(64,101)
Real polynomial:
x^128-1600*x^126+1213760*x^124-582515840*x^122+199073776160*x^120-5169068370\
8800*x^118+10624225316604800*x^116-1777940817532064000*x^114+247285252092074\
994400*x^112-29034513954370783904000*x^110+2913168755228242567712000*x^108-2\
52228081784234462296640000*x^106+18995679239308716650032752000*x^104-1252583\
032266510848451748800000*x^102+72716827232310468063025202880000*x^100-373378\
9294351709468683363925120000*x^98+170236814972276429521470760633880000*x^96-\
6915008067137616880235203234691200000*x^94+250956299821519317016053935487350\
400000*x^92-8156705065169989626518022752369875200000*x^90+237917092173354933\
813459830376585595200000*x^88-6238354345998531992937603564939751904000000*x^\
86+147250862030290486926292969649503772000000000*x^84-3132425082677373214638\
853189903333084480000000*x^82+6010637225053926690525441428838849219872800000\
0*x^80-1041012805002900370842409590722723650342720000000*x^78+16280500640742\
187095522107070825644871855680000000*x^76-2299540377328809362866660421355571\
63330686080000000*x^74+2933382696557829258802171431929376507813649760000000*\
x^72-33787201454731253036956170048169166451291952000000000*x^70+351238388486\
275974312080714758305158377435683200000000*x^68-3293344895367207944986591556\
292978078556732217600000000*x^66+2782819766984106767090559067358235363077861\
4650200000000*x^64-211679739864603642335919722161027381482650585568000000000\
*x^62+1447632907619876826974625398813428073235191570016000000000*x^60-888718\
1054229788025788289162235055410358801840064000000000*x^58+488920545799826302\
86611326562112037147741812010992000000000*x^56-24055924900687629523849892359\
4350379780118896182080000000000*x^54+105621565237119317893293517530513094568\
9321464365120000000000*x^52-412820732615520508786397556781750454464725511884\
4800000000000*x^50+143242742406039923871072621212513230237211475046048800000\
00000*x^48-43994653576155935948432435489780917813791910188336000000000000*x^\
46+119218752107802554639828880787852247954731108548259200000000000*x^44-2840\
47718204329065014489261539842645300166787088864000000000000*x^42+59279176003\
2106606024438891580617319818179301353979200000000000*x^40-107921270723637322\
0903625069234003506687740905899296000000000000*x^38+170643221049248467722266\
6582481148489014831461234592000000000000*x^36-233218168995251244417599018296\
4171281765517024339904000000000000*x^34+274057115593958536761701037695686080\
1903304000504220000000000000*x^32-275293203039947226917316945233645964742062\
0290811840000000000000*x^30+234851901938205143666156698821363584963659925106\
9120000000000000*x^28-168899003322618908497071919976804459179758314356416000\
0000000000*x^26+101533017286982539900568153562315577147377903826800000000000\
0000*x^24-505174374996637766281468259089974704604933877468800000000000000*x^\
22+205617824182017890871184930274656897300255455926400000000000000*x^20-6751\
4383466760121549778673204625910352127620038400000000000000*x^18+175819301847\
04118024432206437495512875479855986400000000000000*x^16-35557771248428310677\
38152445421493206029057632000000000000000*x^14+54381634937420535755121675119\
9216603224227552000000000000000*x^12-607657831230048869513042787679378047615\
55392000000000000000*x^10+47381795108004106090806298386250119525280800000000\
00000000*x^8-242041156715981967135804875512963326634560000000000000000*x^6+7\
406545015703136306531612204210524178240000000000000000*x^4-11880139831095816\
8354013860287290487680000000000000000*x^2+7389512846209712248834462919449280\
10000000000000000
Common denominator of the automorphisms:
1264647478665178577622982064465710269663095410663699107868531039987287907264\
2560977093488501851664804548757584010308872660277289521914522407996412017985\
9481315734880493249173431659953855482838225528452087119086036551602008410479\
2161727191021223719325054663423531033657305514189144508481513361005606549875\
5891560612720405691251490031893422284207339459984292774567458213311127786803\
0310774844130200345511848451892206793516177405541965983573018656348882912076\
8871439131120055273980729492426538172607868195197970152574383756047135251804\
9245989365523882827582341152587604839462972226502664525563665575856816410029\
5945931907412322827600832256849978592460243524946498903724379609588448624640\
00000000000000
Complex polynomial:
x^128+1600*x^126+1213760*x^124+582515840*x^122+199073776160*x^120+5169068370\
8800*x^118+10624225316604800*x^116+1777940817532064000*x^114+247285252092074\
994400*x^112+29034513954370783904000*x^110+2913168755228242567712000*x^108+2\
52228081784234462296640000*x^106+18995679239308716650032752000*x^104+1252583\
032266510848451748800000*x^102+72716827232310468063025202880000*x^100+373378\
9294351709468683363925120000*x^98+170236814972276429521470760633880000*x^96+\
6915008067137616880235203234691200000*x^94+250956299821519317016053935487350\
400000*x^92+8156705065169989626518022752369875200000*x^90+237917092173354933\
813459830376585595200000*x^88+6238354345998531992937603564939751904000000*x^\
86+147250862030290486926292969649503772000000000*x^84+3132425082677373214638\
853189903333084480000000*x^82+6010637225053926690525441428838849219872800000\
0*x^80+1041012805002900370842409590722723650342720000000*x^78+16280500640742\
187095522107070825644871855680000000*x^76+2299540377328809362866660421355571\
63330686080000000*x^74+2933382696557829258802171431929376507813649760000000*\
x^72+33787201454731253036956170048169166451291952000000000*x^70+351238388486\
275974312080714758305158377435683200000000*x^68+3293344895367207944986591556\
292978078556732217600000000*x^66+2782819766984106767090559067358235363077861\
4650200000000*x^64+211679739864603642335919722161027381482650585568000000000\
*x^62+1447632907619876826974625398813428073235191570016000000000*x^60+888718\
1054229788025788289162235055410358801840064000000000*x^58+488920545799826302\
86611326562112037147741812010992000000000*x^56+24055924900687629523849892359\
4350379780118896182080000000000*x^54+105621565237119317893293517530513094568\
9321464365120000000000*x^52+412820732615520508786397556781750454464725511884\
4800000000000*x^50+143242742406039923871072621212513230237211475046048800000\
00000*x^48+43994653576155935948432435489780917813791910188336000000000000*x^\
46+119218752107802554639828880787852247954731108548259200000000000*x^44+2840\
47718204329065014489261539842645300166787088864000000000000*x^42+59279176003\
2106606024438891580617319818179301353979200000000000*x^40+107921270723637322\
0903625069234003506687740905899296000000000000*x^38+170643221049248467722266\
6582481148489014831461234592000000000000*x^36+233218168995251244417599018296\
4171281765517024339904000000000000*x^34+274057115593958536761701037695686080\
1903304000504220000000000000*x^32+275293203039947226917316945233645964742062\
0290811840000000000000*x^30+234851901938205143666156698821363584963659925106\
9120000000000000*x^28+168899003322618908497071919976804459179758314356416000\
0000000000*x^26+101533017286982539900568153562315577147377903826800000000000\
0000*x^24+505174374996637766281468259089974704604933877468800000000000000*x^\
22+205617824182017890871184930274656897300255455926400000000000000*x^20+6751\
4383466760121549778673204625910352127620038400000000000000*x^18+175819301847\
04118024432206437495512875479855986400000000000000*x^16+35557771248428310677\
38152445421493206029057632000000000000000*x^14+54381634937420535755121675119\
9216603224227552000000000000000*x^12+607657831230048869513042787679378047615\
55392000000000000000*x^10+47381795108004106090806298386250119525280800000000\
00000000*x^8+242041156715981967135804875512963326634560000000000000000*x^6+7\
406545015703136306531612204210524178240000000000000000*x^4+11880139831095816\
8354013860287290487680000000000000000*x^2+7389512846209712248834462919449280\
10000000000000000
Common denominator of the automorphisms:
1264647478665178577622982064465710269663095410663699107868531039987287907264\
2560977093488501851664804548757584010308872660277289521914522407996412017985\
9481315734880493249173431659953855482838225528452087119086036551602008410479\
2161727191021223719325054663423531033657305514189144508481513361005606549875\
5891560612720405691251490031893422284207339459984292774567458213311127786803\
0310774844130200345511848451892206793516177405541965983573018656348882912076\
8871439131120055273980729492426538172607868195197970152574383756047135251804\
9245989365523882827582341152587604839462972226502664525563665575856816410029\
5945931907412322827600832256849978592460243524946498903724379609588448624640\
00000000000000
Database of Galois polynomials by Bill Allombert and Igor Schein.
Last Modified: Sat, 16 Jun 2018 12:23:16 +0200
Copyleft © 2002-2008 the PARI group.